Abstract
The paper analyses a relationship between monetary aggregate M2 and inflation in a small open economy. The relationship between monetary expansion and inflation as well as the framework of dynamics income velocity of money in a small open economy are discussed in greater detail in the paper. The authors have developed a monetary model using the empirical verification of the relationship between monetary aggregate M2 and price development in tradable and non-tradable goods and services in the Czech Republic in the period 1996–2007.
The empirical results of the model indicate that money has a significant impact on the price development of non-tradable goods and services.
Keywords: inflation, monetary model, monetary policy, cointegration analysis
JEL: C32, E52, F31, F41
Streszczenie
W niniejszej pracy poddano analizie związek pomiędzy agregatem pieniężnym M2 a inflacją w małej gospodarce o charakterze otwartym. W artykule szczegółowo omawia się związek między ekspansją pieniężną a inflacją, a także ramowy kontekst zmian szybkości dochodowego obiegu pieniądza. Autorzy opracowali model monetarny, poddając empirycznej weryfikacji związek pomiędzy agregatem pieniężnym M2 a ewolucją cen dóbr i usług handlowych i niehandlowych w Czechach w latach 1996–2007. Empiryczne wyniki tego modelu wskazują na znaczące oddziaływanie pieniądza na ewolucję cen dóbr i usług niehandlowych.
Słowa kluczowe: inflacja, model monetarny, polityka pieniężna, analiza kointegracji
Monetary Approach to Inflation – Model of Inflation in a Small Open Economy
and its Application to the Czech Republic in the Period 199–2007 * PodejÊcie monetarne do kwestii inflacji. Model inflacji w małej, otwartej gospodarce i jego
zastosowanie w Czechach w latach 199–2007
Martin Mandel
**, Vladimír Tomšík
***received: 13 May 2008, final version received: 6 October 2008, accepted: 29 October 2008
* The paper was supported by Grant Agency of the Czech Republic, Project 402/06/0209. The text contains the authors’ opinions that need not necessarily reflect or be consistent with the official opinions of the Czech National Bank.
** University of Economics in Prague; e-mail: mandel@vse.cz
*** Czech National Bank; e-mail: vladimir.tomsik@cnb.cz
1. Introduction
“Small” macroeconomic simulation models used in monetary policy for which the name inflation targeting has become accepted usage are based on the post- Keynesian theory (of the so-called horizontalists) about the absolute endogeneity of money in the medium and long run.1 According to this concept, money in economic relations is a “residual” item that cannot generate inflation pressures. The own model of inflation targeting is mainly based on the theory of “New Keynesians”
who do not consider inflation primarily as a monetary phenomenon either.
In a simplified form, models of inflation targeting comprise the IS curve. They also contain a modified and augmented version of the Phillips curve as the relationship of inflation to output gap and inflation expectations. Uncovered interest rate parity and yield curve describing the time structure of interest rates are also usually parts of the model.2 The execution of monetary policy is based on the management of short run interest rate through repo operations of the central bank. If money is not included in simulation models used for inflation forecasting, it means that the active role of money in influencing the price level development is not assumed in terms of the model. Money is a variable passively adjusting itself in relationship to real and price processes. Such an assumption is hardly acceptable for a monetary economist and contradicts historical experience. Empirical research mostly confirms Friedman’s statement that “inflation is always and everywhere a monetary phenomenon” (Friedman 1963).3
Models of “New Keynesians” based on the so-called gap form4 face a lot of both theoretical and practical problems at the same time. Particularly, it is a problem of a huge number of the unobservable variables included into a model (natural equilibrium of real exchange
1 In a narrow meaning, the debate on an endogenity of money is a debate on whether the money base (respectively money supply) is really controlled by a central bank. In a broad meaning, it is a debate on the direction and the causality of the monetary transmission mechanism. The followers of Kaldor (1982) and Moore (1988) argue that money supply is fully determined by the previous credit demand which depends on an investment demand as well as on a cash-flow capital demand. In that case, the money supply in the whole inflation process is only a “passive” variable which can even be omitted in the models of inflation.
2 The number of equations (including identities) in models of inflation targeting usually ranges between 15 and 20 (e.g. Beneš et al. 2002; Kotlán 2002; Hlédik 2004).
3 De Grauwe and Polan (2005) show that there is a strong relationship between the growth of nominal money supply and inflation in the countries with high inflation. On the other hand, they show the tested relationship is not strong in the countries that have average inflation less then 10%. Nevertheless, it is ques- tionable whether it is correct to test the low and high inflationary countries sepa- rately. These doubts come from a statistical fact that the low variability of a vari- able results into a low statistical significance of empirical estimations. It should be added that De Grauwe and Polan obtained their results running cross-country and panel analyses which were carried out with a dataset of 160 countries and include the time period of 1969–1999.
4 The “gap” is to be taken as the difference between the actual and equilibrium variable in a logarithmic form.
rate, natural equilibrium of real interest rate, natural rate of unemployment, potential product, expected inflation, expected exchange rate, and risk premium in the uncovered interest rate parity as well as in the yield curve). The natural equilibriums of these real variables are not defined as unambiguous in view of both the theoretical and the empirical concepts. Their contents, if they are to make sense, are connected with the specific formulation of the model. Theoretical economic schools hold the debate whether the natural equilibriums of the real variables are stable. Their stability is questionable especially in transition countries. It poses a serious question whether a combination of purely statistical procedures as filtering off deviations of the observed variables, calibration using information for more mature economics, using great ratios, etc., could solve this problem.
Similar problems also arise when we want to include expected variables in the model (e.g. expected exchange rate under uncovered interest rate parity, expected inflation at the real interest rate). The principle of rational expectations excludes the description of behaviour by one “universally valid” fundamental model because each agent in the market has their individual model. “Small” macroeconomic simulation models use a concept of “model consistent expectations”.5 This approach enables a model implementation of the forward-looking expectations. Nevertheless, we are afraid that this approach doesn’t solve the problem that rational economic agents may form their expectations using different models than the “New Keynesian” models are using. It cannot be ruled out that the expectations of each agent in the market could be formed in a different way than it is predicted by the model.
Theoretical (whether Keynesian or monetarist) purity of a model becomes a “burden” for the practical realisation of monetary policy when the initial postulations of the theory are not satisfied or when we are not able to fill the theoretically correct model with required data. In these cases, prediction results of the “main” model should always be confronted with the development of the so-called monetary indicators. In particular, these are indicators describing the “off-model” area. In models of inflation targeting, these are mainly quantity monetary variables (i.e. monetary aggregates).
The objective of this paper is to analyse a relationship between the development of money supply (monetary aggregate M1 and M2) and the price level fluctuation in the Czech Republic as the case of a small open transition economy. We ask a question whether an increase in the money supply in excess of the real gross domestic product may be a significant signal of future inflationary development. We react to an empirically observed fact that
5 The model-consistent expectations of variable X in their reduced form are formed only by exogenous (respectively predetermined) variables which are in- cluded in the model.
the growth rates of monetary aggregate M2 in the Czech Republic in 2004-2007 (annual growth rate) gradually increased from 5.8% to 17%. Our approach enlarges the original monetarist transmission mechanism of the monetary policy which was formulated by Friedman (1956; 1960; 1963). Our model deals with the conditions of a small open economy and it also stresses a difference of the transmission price mechanism for tradable and non-tradable goods and services.
Part 2 contains a theoretical exposition of the relationship between monetary expansion and inflation in the short, medium and long run. Emphasis is laid on the explanation of the dynamics of income velocity of money and on its economic substantiation in conditions of an open economy. In Part 3, a monetary model of inflation is formulated for the relationship between the development of money supply and prices of internationally tradable and non-tradable goods.
Part 4 presents econometric verification of the model, statistical and economic evaluation of the results.
2. Monetary approach to inflation
– interpretation of the dynamics of income velocity of money
Traditional “textbook” graphs on which Fisher’s (1922) and Friedman’s approaches to the long-run inflation are demonstrated correlate average annual growth rates of money supply with average annual inflation rate in particular countries. Interpretation of these graphs is usually based on a comparatively static approach within a closed economy.6 Our dynamic monetary model in a small open economy will be derived from Friedman’s hypothesis about the lag of real growth and inflation behind monetary expansion. This hypothesis makes it possible to develop a discussion about the phases of inflation process in an open economy.
Formally, the model is based on the quantity equation of exchange modified for real gross domestic product7
PY MVY
Y T VY VT
SR SR
Y M
Vˆ, ˆ
MR MR MR
Y Y M
Vˆ, ˆ ˆ
LR Y LR LR
LR M Y V
Pˆ ˆ ˆ ˆ, E E
E M Y
Pˆ ˆ ˆ
MR MR
MR MR
Y M
Y
IM EX G I M C
Y
Vˆ, ˆ ˆ ' ' ' ' ' ˆ IM
EX G I C
Y ' ' ' ' ' '
)
2(
,t tk
T f ER
P ,
)
3(
l t
l
t Y t
f NCA ER
,
)
4(
m t
m t t
t
Y f M Y NCA
)
1(
, tn
n t t
NT Y
f M P
k T12 ln2
where we assume that the real gross domestic product (Y) is at a constant ratio to the total volume of economic transactions (T). So the income velocity of money (VY) is expressed by the equation PYMVY
Y T VY VT
SR SR
Y M
Vˆ, ˆ
MR MR MR
Y Y M
Vˆ, ˆ ˆ
LR Y LR LR
LR M Y V
Pˆ ˆ ˆ ˆ,
E E
E M Y
Pˆ ˆ ˆ
MR MR
MR MR
Y M
Y
IM EX G I M C
Y
Vˆ ˆ ˆ ˆ
, ' ' ' ' '
IM EX G I C
Y ' ' ' ' ' '
)
2(
,t tk
T f ER
P ,
)
3(
l t
l
t Y t
f NCA ER
,
)
4(
m t
m t t
t
Y f M Y NCA
)
1(
,
n t
n t t
NT Y
f M P
k T12 ln2
6 A dynamic model of inflation based on the quantity equation of exchange was developed for the first time by Cagan (1956). Klaus (1988) formulated a dynamic model for conditions of centrally planned economy with inflexible prices. The dynamics of monetary inflation process is also studied by Kodera and Tran (2008) and Husár and Szomolanyi (2008). However, all above-mentioned ap- proaches and models operate in conditions of a closed economy.
7 We assume the equality between real product and real income in this paper.
where VT is original Fisher’s transaction velocity of money.
2.1. The case of a closed economy
Let us assume that the central bank under the impression of economic recession will “admit” or “select” the policy with a long run high growth rate of money supply.
Friedman’s lag of the real product or price level behind the money supply contains important implicit information on the behaviour of income velocity of money in the “short”
run. As in the period of “looking around” the economic agents do not immediately increase their demand for goods and services, the income velocity of money (calculated ex post) decreases with monetary expansion. In the short run (subscript SR), the relative change in income velocity of money equals the relative change in money supply
PY MVY
Y T VY VT
SR SR
Y M
Vˆ, ˆ
MR MR MR
Y Y M
Vˆ, ˆ ˆ
LR Y LR LR
LR M Y V
Pˆ ˆ ˆ ˆ, E E
E M Y
Pˆ ˆ ˆ
MR MR
MR MR
Y Y M C I GY EX IM M
Vˆ, ˆ ˆ ' ' ' ' ' ˆ IM
EX G I C
Y ' ' ' ' ' '
)
2(
,t t k
T f ER
P ,
)
3(
l t
l
t Y t
f NCA ER
,
)
4(
m t
m t t
t
Y f M Y NCA
)
1(
,
n t
n t t
NT Y
f M P
k T12 ln2
where the caret is a symbol of relative change.
This fact is accentuated mainly by supporters of the so-called theory of money endogeneity (e.g. Rousseas 1960; Davidson 1974) who consider a decline in the income velocity of money under monetary expansion as a proof of the inefficiency of monetarist monetary policy to influence the side of aggregate demand. But the monetarists take a decline in the income velocity of money as temporary only. An increase in the real money balances will motivate with some lag the agents to increase their demand for goods and services (the so- called direct channel).
In the medium run (subscript MR), the demand will increase and the real product will grow. But the income velocity may continue to decline also in this period. It will be the case when:
a) a part of consumer demand is satisfied by the sale of goods from the stocks of finished products,
b) the previously granted business loans in the framework of supplier-customer relations are quickly paid back.
In the “medium” run, it holds good that the relative change in the income velocity of money equals a difference between the growth rate of real product and growth rate of money supply
PY MVY
Y T VY VT
SR SR
Y M
Vˆ, ˆ
MR MR MR
Y Y M
Vˆ, ˆ ˆ
LR Y LR LR
LR M Y V
Pˆ ˆ ˆ ˆ,
E E
E M Y
Pˆ ˆ ˆ
MR MR
MR MR
Y M
Y
IM EX G I M C
Y
Vˆ ˆ ˆ ˆ
, ' ' ' ' '
IM EX G I C
Y ' ' ' ' ' '
)
2(
,t tk
T f ER
P ,
)
3(
l t
l
t Y t
f NCA ER
,
)
4(
m t
m t t
t Y
f M Y NCA
)
1(
,
n t
n t t
NT Y
f M P
k T12 ln2
In the long run (subscript LR), the continuing excessive monetary expansion leads to the growth of price level in two stages. In the first stage, there is a
“shock” jump of inflation because the income velocity of money returns to its original equilibrium level. This equation holds good for domestic inflation (i.e. for the relative change in the domestic price level)
PY MVY
Y T VY VT
SR SR
Y M
Vˆ, ˆ
MR MR MR
Y Y M
Vˆ, ˆ ˆ
LR Y LR LR
LR M Y V
Pˆ ˆ ˆ ˆ,
E E
E M Y
Pˆ ˆ ˆ
MR MR
MR MR
Y M
Y
IM EX G I M C
Y
Vˆ, ˆ ˆ ' ' ' ' ' ˆ IM
EX G I C
Y ' ' ' ' ' '
)
2(
,t tk
T f ER
P ,
)
3(
l t
l
t Y t
f NCA ER
,
)
4(
m t
m t t
t Y
f M Y NCA
)
1(
, tn
n t t
NT Y
f M P
k T12 ln2
In the second stage, when the economy has already reached the equilibrium trajectory (subscript E), the price level goes up only in relation to a difference between the relative growth of money supply and real product
SR SR
Y M
Vˆ, ˆ
MR MR MR
Y Y M
Vˆ, ˆ ˆ
LR Y LR LR
LR M Y V
Pˆ ˆ ˆ ˆ,
E E
E M Y
Pˆ ˆ ˆ
MR MR
MR MR
Y M
Y EX IM G
I M C
Y
Vˆ ˆ ˆ ˆ
, ' ' ' ' '
IM EX G I C
Y ' ' ' ' ' '
)
2(
,t tk
T f ER
P ,
)
3(
l t
l
t Y t
f NCA ER
,
)
4(
m t
m t t
t
Y f M Y NCA
)
1(
,
n t
n t t
NT Y
f M P
k T12 ln2
According to the monetarist “long run” approach, inflation on the long run average corresponds to the growth rate of nominal money supply in excess of the growth rate of gross domestic product.
2.2. The case of an open economy
A monetary approach to the balance of payments (e.g. Polak 1957; Johnson 1977)8, which assumes the existence of fixed exchange rates, offers another alternative explanation of a decline in the ex-post calculated income velocity of money in the medium run. In an open economy, monetary expansion may be accompanied in the medium run by the growth of goods and services imports and by the worsening of the balance of payments. From the aspect of an expenditure approach to the calculation of gross domestic product, the growth of imports (ΔIM>0) is balanced by the growth of private consumption (ΔC>0) while the gross domestic product does not change (ΔY=0). A decline in the ex-post calculated income velocity of money in a small open economy is the result of these processes9
PY MVY
Y TV VY T
SR SR
Y M
Vˆ, ˆ
MR MR MR
Y Y M
Vˆ, ˆ ˆ
LR Y LR LR
LR M Y V
Pˆ ˆ ˆ ˆ, E E
E M Y
Pˆ ˆ ˆ
MR MR
MR MR
Y M
Y
IM EX G I M C
Y
Vˆ, ˆ ˆ ' ' ' ' ' ˆ IM
EX G I C
Y ' ' ' ' ' '
)
2(
,t tk
T f ER
P ,
)
3(
l t
l t t
Y f NCA ER
,
)
4(
m t
m t t
t
Y f M Y NCA
)
1(
, n t
n t t
NT Y
f M P
k
T12 ln2 where the relation
PY MVY
Y T VY VT
SR SR
Y M
Vˆ, ˆ
MR MR MR
Y Y M
Vˆ, ˆ ˆ
LR Y LR LR
LR M Y V
Pˆ ˆ ˆ ˆ, E E
E M Y
Pˆ ˆ ˆ
MR MR
MR MR
Y M
Y
IM EX G I M C
Y
Vˆ, ˆ ˆ ' ' ' ' ' ˆ IM
EX G I C
Y ' ' ' ' ' '
)
2(
,t tk
T f ER
P ,
)
3(
l t
l
t Y t
f NCA ER
,
)
4(
m t
m t t
t
Y f M Y NCA
)
1(
, n t
n t t
NT Y
f M P
k T12 ln2
is valid for a change in the gross domestic product.
It may seem for quite a long time that from the aspect of a small open economy, the world economy creates the “infinitely elastic” supply of goods and services, which makes it possible to maintain the stable domestic price level (and/or low inflation). In the long run, the imbalanced monetary expansion is however connected with a monetary crisis sooner or later while the exceeding of the acceptable level of foreign indebtedness of a country is its immediate cause.10 After domestic currency devaluation, the price level is adjusted by “a jump” again.
8 Research on this problem in Czech conditions was conducted e.g. by Kodera and Mandel (1995), Frait (1996) and Tomšík (2000).
9 E.g. in the period from the 2nd half of 1993 to the 1st half of 1996 the year- on-year growth rates of monetary aggregate M2 were considerably high in the CR, approximately at the level of 20%. But the deficit of the balance of pay- ments current account increased from the original surplus of +13 billion CZK in 1993 to the deficit of -117 billion CZK in 1996. In the same period, the inflation measured by consumer price index paradoxically decreased from 18.2% (1993) to 8.6% (1996).
10 International financial markets monitor especially the ratio indicator gross foreign debt to gross domestic product that should not increase above 40% in its percentage expression. It has to be noted that just before the monetary crisis in May 1997, the CR reached this critical value.
In the systems of floating exchange rates, the adjustment of exchange rates and prices to the imbalanced monetary expansion should be more flexible, in accordance with the relative version of purchasing power parity and with the so-called monetary approach to the exchange rate. A longer lag between the growth of money supply and the exchange rate (and/or price) reaction may occur when there is a parallel influx of foreign capital providing the sufficient supply of foreign exchange.
3. Structural dynamic monetary model of inflation in a small open economy
A structural monetary model of inflation in a small open economy should be based on the separate analysis of price development in internationally tradable goods and internationally non-tradable goods. Data in Table 1 document that the price indices in the CR show markedly different dynamics in the sectors of internationally tradable goods and internationally non-tradable goods.11 The prices of internationally non-tradable goods have been rising faster than the prices of internationally tradable goods in the long run.
The differentiation of these two groups of goods is economically justified in view of a structural monetary model. In the sector of internationally tradable goods, monetary expansion should not immediately lead to the price level growth because a small open economy is in the position of price taker and faces the infinitely elastic foreign supply of goods and services. In agreement with the monetary approach to the balance of payments, monetary expansion leads to the worsening of net trade balance (and/or net current account) in the first stage. The price level growth follows the depreciation of exchange rate that is a reaction to the deficit of trade balance (and/or current account) and growth of foreign indebtedness of the country.
In the price index of internationally tradable goods, (PT) total lag is given by:
a) the reaction time of net current account (NCA) development to money supply (M) development,
b) the reaction time of exchange rate (ER) development to net current account (NCA) development,
c) the reaction time of the price index development of internationally tradable goods (PT) to exchange rate (ER) development.12
11 In accordance with the Czech National Bank’s classification, services are con- sidered as internationally non-tradable goods whereas merchandise is considered as tradable goods. Non-tradable goods are further divided into regulated ones and others. Regulated services comprise e.g. rent control in residential housing, regula- tion of water tariffs and sewage disposal charges, refuse disposal, urban mass trans- portation, electricity and gas supplies, health care, education and some other serv- ices. The other (unregulated) non-tradable goods involve e.g. couture, uncontrolled renting of residential housing, repair services, air transport, recreation and culture, boarding and lodging, hairdresser services, insurance and other financial services.
12 The relationship between exchange rate changes and inflation in the transi- tion countries is examined for example by Ca`Zorzi et al. (2007). The older lit- erature but directly focused on the Czech (respectively Czechoslovak) economy is for example Holub (1999) and Mandel (1992).
These three lags are formally expressed by the following three functional relations13
PY MVY
Y T VY VT
SR SR
Y M
Vˆ, ˆ
MR MR MR
Y Y M
Vˆ, ˆ ˆ
LR Y LR LR
LR M Y V
Pˆ ˆ ˆ ˆ, E E
E M Y
Pˆ ˆ ˆ
MR MR
MR MR
Y M
Y
IM EX G I M C
Y
Vˆ, ˆ ˆ ' ' ' ' ' ˆ IM
EX G I C
Y ' ' ' ' ' '
)
2(
,t tk
T f ER
P ,
)
3(
l t
l t t
Y f NCA ER
,
)
4(
m t
m t t
t
Y f M Y NCA
)
1(
, n t
n t t
NT Y
f M P
k
T12 ln2
A straighter and shorter pathway between monetary expansion and price growth is to be expected in the prices of internationally non-tradable goods where domestic prices are not directly anchored to foreign prices. Price movement in this sector will apparently react much faster to changes in domestic demand. Let us assume a lag of only several quarters of the year between money supply development (M) and development of the price index of international non-tradable goods (PNT)
PY MVY
Y T VY VT
SR SR
Y M
Vˆ, ˆ
MR MR MR
Y Y M
Vˆ, ˆ ˆ
LR Y LR LR
LR M Y V
Pˆ ˆ ˆ ˆ, E E
E M Y
Pˆ ˆ ˆ
MR MR
MR MR
Y M
Y
IM EX G I M C
Y
Vˆ, ˆ ˆ ' ' ' ' ' ˆ IM
EX G I C
Y ' ' ' ' ' '
)
2(
,t tk
T f ER
P ,
)
3(
l t
l
t Y t
f NCA ER
,
)
4(
m t
m t t
t
Y f M Y NCA
)
1(
, n t
n t t
NT Y
f M P
k T12 ln2
In the following part, the hypothesis about a different influence of money supply on prices in the sectors of internationally tradable and internationally non-tradable goods is tested by cointegration analysis.
13 The econometric form of a similar structural model for the Czech economy for the period of the 1st quarter of 1996 to the 4th quarter of 2004 was economet- rically tested with success by the vector autoregression model (VAR model) in Arlt et al. (2006) and it confirmed statistical significance of all key relationships and causal linkages from the aspect of the so-called time causality.
4. Testing of long run equilibrium relations in a monetary model
The simplest approach to empirical verification of a monetarist model of inflation is based on the analysis of the relationship between the development of the aggregate price level (consumer price index, quarterly frequency of time series) and the growth of nominal money supply in excess of the growth of gross domestic product by means of correlation
Table 1. Price development in the sectors of internationally tradable and non-tradable
goods (end of the period, %)
1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 Average of1993–
2007 Consumer prices
(100% in total) 18.2 10.2 7.9 8.6 10.0 6.8 2.5 4.0 4.1 0.6 1.0 2.8 2.2 1.7 5.4 6.1
Tradable goods and se- rvices
(51.4% share) 15.5 9.1 6.4 6.6 6.3 0.7 1.3 2.3 0.4 -2.6 0.1 0.2 -0.8 0.0 7.0 3.6
Non-tradable goods and services
(48.6% share) 23.5 10.5 10.6 11.8 16.8 16.8 4.3 6.3 8.6 3.9 2.0 5.5 4.9 3.4 3.9 9.3
Sources: Czech Statistical Office (CSO) and CNB.
Table 2. Granger causality tests
Null Hypothesis:
X does not Granger-cause Y Lag Obs. F-statistics Probability
M2/GDP → CPI 2 45 4.8594 0.0129
CPI → M2/GDP 2 45 1.8594 0.1690
M2/GDP → CPI 4 43 2.53741 0.0579
CPI → M2/GDP 4 43 0.9292 0.4586
Note: The time series are adjusted for their trend by means of the Hodrick-Prescott filter, so they are stationary.
Figure 1. Consumer Price Index and the
growth of nominal money supply in excess of the growth of Gross Domestic Product
Sources: CSO and CNB.
0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
Q1 1996Q1
1997 Q1 1998 Q1
1999 Q1 2000 Q1
2001Q1 2002Q1
2003Q1 2004 Q1
2005 Q1 2006 Q1
2007 Price level (cumulative growth of consumer prices)
M2 growth rate in excess of real GDP growth rate
Trend of price level development Trend of M2 growth in excess of GDP growth
Q3 Q3 Q3 Q3 Q3 Q3 Q3 Q3 Q3 Q3 Q3 Q3
coefficients.14 Figure 1 shows the development of these two variables in 1996–2007.
As expected, the value of the correlation coefficient (0.985) is very high in this case. It is however problematic that the correlation coefficient is calculated from non- stationary time series that may involve the so-called
“spurious causality”. For this reason we adjusted the time series for their trend by means of the Hodrick- Prescott filter. Subsequently, correlation coefficients for residual values were estimated (see Figure 2).
The correlation coefficient 0.356 is also positive in this case (no lag is used). The following correlation coefficients were obtained once we ran cross correlation analysis using time lags from t-0 to t-6: 0.356, 0.396, 0.368, 0.287, 0.230, 0.145, and 0.008. And Table 2 shows results of the Granger causality tests using time lags from t-2 to t-4.
The results of the performed Granger causality tests published in Table 2 show that there is a one-way
14 We also run the tests using monetary aggregate M1. However, the obtained econometric results were not statistically significant. We also wanted to run the tests using monetary aggregate M3 but this broad monetary aggregate is not available from 1996. The Czech National Bank started reporting monetary ag- gregate M3 in 2002.
relationship between the excess of M2/GDP and inflation measured by consumer price index. This relationship has been predicted by monetarists.
The statistical methods using the time series which are adjusted for their trend by means of the Hodrick- Prescott filter confirm the expected relationship between money supply (aggregate M2) and inflation in both the short and medium run. A disadvantage of this approach is that by adjusting the time series for their trend we lose a possibility of testing the long-run relationships between the studied variables.
However, the monetarist approach to inflation accentuates relationships in the long run. Therefore, we proceed to the cointegration analysis and to the estimate of the error correction model. In comparison with the traditional regression and correlation analysis (based on the least-squares method), an advantage of this method of econometric analysis is that it enables to test the long run equilibrium relationships without risk of the so- called spurious causality if the given conditions for the time series integration are satisfied. In accordance with our hypothesis about a different inflation influence of money supply growth, we proceed to the desaggregation
Figure 2. Residuals after adjustment of the
time series for their trend
Sources: CSO and CNB.
-0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05
Residuals of inflation and trend Residuals of the excess of M2/GDP and trend
Q1 Q3 1996 Q1 Q3
1997 Q1 Q3 1998 Q1 Q3
1999 Q1 Q3 2000 Q1 Q3
2001 Q1 Q3 2002 Q1 Q3
2003 Q1 Q3 2004 Q1 Q3
2005 Q1 Q3 2006 Q1 Q3
2007
Figure 3. Development of Money Supply
Index and Price Indices for 1996–2007
Sources: CNB, CSO and own calculations.
0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50
M2 M2 to real GDP ratio Prices – internat. non-tradable goods Prices – internat. tradable goods
III1996IX III IX III IX III IX III IX III IX III IX III IX III IX III IX III IX III IX1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
Table 3. Results of the Augmented Dickey-Fuller Unit Root Test
Variable Level data
(t-statistics)
First difference (t-statistics)
Monetary aggregate M2 to real GDP ratio (M2/Y) -1.5842 -6.3519
Prices of internationally non-tradable goods (PNT) -2.3299 -6.7680
Prices of internationally tradable goods
(PT) -2.2776 -4.4938
Prices of consumer goods (P) -2.5516 -4.8531
Note: Critical values at a 1% and 5% significance level for the respective number of observations are -3.5812 and -2.9266 for the first column, and -3.5847 and -2.9281 for the second column.
of consumer price index into prices of internationally tradable and non-tradable goods.
Figure 3 illustrates development of the base index of money supply (monetary aggregate M2), development of the growth of nominal money supply in excess of the growth of gross domestic product and development of base price indexes (prices of internationally tradable and non-tradable goods) for the period 1996-2007 (quarterly frequency).
The figure documents that these are non-stationary time series where it is not possible to use “with impunity”
the traditional regression and correlation analysis based on the least-squares method. The augmented Dickey- Fuller unit root test (Table 3) showed that all examined test series were integrated by degree one I(1), i.e. the first differences of the tested time series are stationary.15 So, we can proceed to the cointegration analysis on the level data; its results are presented in Table 4.
Several important conclusions are drawn on the basis of our results.
Firstly, the prices of internationally non-tradable goods are cointegrated with the development of the monetary aggregate M2 to gross domestic product ratio.
Just one cointegration vector on a 5% significance level was found. It is also important that the statistically significant coefficient of adjustment in the error correction model (k = -0.086) signals that the price level in the sector of internationally non-tradable goods adjusts itself to a monetary shock. The half-time of adjustment is approximately 24 months (i.e. 2 years).16
Secondly, the prices of internationally tradable goods are cointegrated with the development of the monetary aggregate M2 to gross domestic product ratio.
Just one cointegration vector on a 5% significance level
15 We are aware that the power of the ADF test for short samples is usually low and that is why we also run other tests to examine whether the tested time series are stationary or not. We used Phillips-Perron test as well as Kwiatkowski-Phil- lips-Schmidt-Shin test and both tests showed that the tested time series were integrated by degree one I(1), i.e. the first differences of the tested time series are stationary.
16 The half-time of adjustment is calculated from the equation PY MVY
Y TV VY T
SR SR
Y M
Vˆ ˆ
,
MR MR MR
Y Y M
Vˆ ˆ ˆ
,
LR Y LR LR
LR M Y V
Pˆ ˆ ˆ ˆ, E E
E M Y
Pˆ ˆ ˆ
MR MR
MR MR
Y M
Y IM EX G I M C Y
Vˆ, ˆ ˆ ' '' ' ' ˆ IM
EX G I C
Y ' ' ' ' ' '
)
2(
,t tk
T f ER
P ,
)
3(
l t
l
t Yt
f NCA ER
,
)
4(
m t
m t t
t
Y f M Y NCA
)
1(
, tn
n t t
NT f MY
P
k
T12 ln2, where k is the estimated coefficient of adjustment.
was found. But the statistically insignificant coefficient of adjustment in the error correction model signals that in the studied period the price level in the sector of internationally tradable goods did not react to monetary shocks by “sufficiently” fast adjustment.
Thirdly, the prices of consumer goods (i.e. total CPI) are cointegrated with the development of the monetary aggregate M2 to gross domestic product ratio, but on a 10% significance level. The statistically insignificant coefficient of adjustment in the error correction model signals again that in the studied period the total price level did not react to monetary shocks by “sufficiently”
fast adjustment.
5. Conclusion
Our research based on the correlation analysis, Granger causality tests, and the cointegration analysis supports the idea that the variable of money supply in excess of the real product (M2/GDP) is a statistically significant explanatory variable of inflation in the case of the Czech economy in the period of 1996- 2007. It indicates that the variable of money supply M2 can be considered a supplementary variable of inflation pressures in the system in which a central bank carries out inflation targeting programme. The cointegration analysis has verified the idea that there exists a long-run equilibrium relationship between price development and money supply in excess of the real product (M2/GDP). It is to note that this relationship is the strongest for the development of prices of internationally non-tradable goods.
It is also worthy to note that the results reached high statistical significance even though the examined economy had reported low inflation (inflation did not exceed 10% in the Czech economy in the period 1996- 2007). These results do not confirm the pessimism about the relationship between money supply and inflation in low inflationary economies that was expressed by De Grauwe and Polan (2005).
Table 4. Cointegration analysis for the prices of internationally (non)tradable goods
Cointegration relationship Cointegration coefficient
(t-statistics) Number of cointegration vectors Coefficient of adjustment (t-statistics)
PNT and M2/Y -1.437
(-30.280) one
(5% significance level) -0.086
(-3.161)
PT and M2/Y -0.653
(-13.194) one
(5% significance level)
0.006 (0.689)
P and M2/Y -0.969
(-72.396) one
(10% significance level) 0.030
(0.744) Note: As for the form of writing the cointegration equation, the sign minus represents a positive relationship between the tested variables.
